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Understanding the long-term spatial dynamics of a semiarid grass-shrub steppe through inverse parameterization for simulation models

Pablo A. Cipriotti , Mart í n R. Aguiar , Thorsten Wiegand and Jos é M. Paruelo

P. A. Cipriotti (cipriott@agro.uba.ar) and J. M. Paruelo, Depto de M é todos Cuantitativos y Sistemas de Informaci ó n, Facultad de Agronom í a - IFEVA, Univ. de Buenos Aires/CONICET, Argentina. Present address for PAC: Depto de M é todos Cuantitativos y Sistemas de Informaci ó n, Facultad de Agronom í a, Av. San Mart í n 4453 (C1417DSE), Ciudad de Buenos Aires, Argentina. Present address for JMP: Laboratorio de An á lisis Regional y Teledetecci ó n, IFEVA, Facultad de Agronom í a, Univ. de Buenos Aires/CONICET, Argentina. – M. R. Aguiar, C á tedra de Ecolog í a - IFEVA, Depto de Recursos Naturales y Ambiente, Facultad de Agronom í a, Univ. de Buenos Aires/CONICET, Argentina. – T. Wiegand, UFZ Helmholtz Centre for Environmental Research - UFZ, Dept of Ecological Modelling, Permoserstra ß e 15, DE-04318 Leipzig, Germany .

Desertifi cation threatens 70% of all dry lands worldwide by diminishing the provision of economic and ecosystem services. However, since long-term vegetation dynamics of semiarid ecosystems are diffi cult to study, the opportunities to evaluate desertifi cation and degradation properly are limited. In this study, we tailored, calibrated and tested a spatially-explicit simulation model (DINVEG) to describe the long-term dynamics of dominant grass and shrub species in the semiarid Patagonian steppe. We used inverse techniques to identify parameterizations that yield model outputs in agreement with detailed fi eld data, and we performed sensitivity analyses to reveal the main drivers of long-term vegetation dynamics. Whereas many parameterizations (10 – 45%) matched single fi eld observations (e.g. grass and shrub cover, species-specifi c density, aboveground net primary production [ANPP]), only a few parameterizations (0.05%) yielded simultaneous match of all fi eld observations. Sensitivity analysis pointed to demographic constraints for shrubs and grasses in the emergence and recruitment phase, respectively, which contributed to balanced shrub-grass abundances in the long run. Vegetation dynamics of simulations that matched all fi eld observations were characterized by a stochastic equilibrium. Th e soil water content in the top layer (0 – 10 cm) during the emergence period was the strongest predictor of shrub densities and popula-tion growth rates and of growth rates of grasses. Grasses controlled the shrub demography because of the resource overlap of grasses with juvenile shrubs (i.e. water content in the top layer). In agreement with fi eld observations, ecosystem func-tion buff ered the strong variability in precipitation (a simulated CV in ANPP of 16% vs CV in precipitation of 33%). Our results show that seedling emergence and recruitment are critical processes for long-term vegetation dynamics in this steppe. Th e methods presented here could be widely applied when data for direct parameterization of individual-based models are lacking, but data corresponding to model outputs are available. Our modeling methodology can reduce the need for long-term data sets when answering questions regarding community dynamics.

Oikos 121: 848–861, 2012 doi: 10.1111/j.1600-0706.2012.20317.x

© 2012 Th e Authors. Oikos © 2012 Nordic Society Oikos Subject Editor: Eric Seabloom. Accepted 6 January 2012

According to the United Nations (UNEP, Agenda 21), approximately 70% of all dry lands (representing a total area of 3.6 billion hectares, a quarter of the total land surface of the earth) is endangered by desertifi cation. Th e prin-cipal causes are human land use activities and climatic vari-ability in combination with complex ecosystem dynamics (Reynolds and Staff ord Smith 2002, Reynolds et al. 2007). Replacement of grasses by woody plants (trees or shrubs) and changes in the spatial organization of arid rangelands have promoted major changes in biodiversity and ecosystem functioning (e.g. productivity, decomposition and carbon storage, nitrogen and water dynamics) (Schlesinger et al. 1990, Scholes and Archer 1997, Jackson et al. 2000), jeop-ardizing the sustainability of animal husbandry (Sharp and

Whittaker 2003). Th erefore, understanding the processes governing coexistence of diff erent life forms and emergence of spatial patterns is important for predicting how semi-arid plant communities respond to land use (e.g. grazing) and climate change (Sankaran et al. 2004, Tietjen and Jeltsch 2007).

However, understanding patterns and processes of vegetation dynamics in semiarid rangelands is an inherently diffi cult task due to several factors such as the mismatch in time scales between observation and vegetation change, the occurrence of complex event-driven dynamics, spatial heterogeneities, and non-equilibrium ecosystem dynam-ics (Wiegand et al. 1995, Jeltsch et al. 2000, Briske et al. 2003, Peters and Havstad 2006). As a consequence, a purely

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observational or experimental approach is often not feasible. One possibility to overcoming these limitations is the use of individual-based and spatially-explicit computer simula-tion models (Wiegand et al. 1995). Th is approach provides understanding of arid rangeland dynamics by focusing on the processes and mechanisms that drive vegetation dynamics at the level of individual plants. Although there is little availability of long-term fi eld data on full vegetation dynamics, short-term studies often provide data on seedling recruitment, plant growth, reproduction, seed dispersal, and plant – plant interactions. Th e basic approach is to incor-porate the data on individual plant behavior in the form of simple rules into an individual-based model (IBM; Grimm and Railsback 2005) that simulates the fate and the inter-actions of individual plants in a spatially-explicit context (within the community), the sum of which represents com-munity dynamics (Wiegand et al. 1995). Th is approach addresses one of the major challenges in ecology; under-standing how processes at small scales determine patterns at large scales (Levin 1992).

However, data for direct parameterization of individual-based models are usually not available for all parameters and there is often uncertainty in the formulation of mecha-nisms and processes (Wiegand et al. 2003, 2004a, Grimm and Railsback 2005, Hartig et al. 2011). One promising approach for model parameterization is to take advantage of the ability of individual-based models to generate outputs at larger scales such as community composition or average plant cover (called ‘ patterns ’ ; Wiegand et al. 2003, Grimm et al. 2005). Th e task then is to fi nd model structures and parameterizations that generate (larger-scale) outputs con-sistent with the corresponding fi eld data (Wiegand et al. 2004a, Hartig et al. 2011). However, model fi tting is quitechallenging in the case of computationally-demanding models like IBMs (Wiegand et al. 2003, DeAngelis and Mooij 2003, Grimm et al. 2005, Martínez et al. 2011). Additionally, there is no established approach that would parallel model selection for statistical models (Burnham and Anderson 2002; but see Wood 2010, Hartig et al. 2011, Martínez et al. 2011).

To overcome these diffi culties, we used inverse tech-niques of pattern-oriented modeling (Wiegand et al. 2003, 2004a, Grimm et al. 2005, Kramer-Schadt et al. 2007, Hartig et al. 2011) to fi t a model to larger scale data. Th is approach required model simulations over the entire param-eter space. Suitable parameterizations were detected by a multiple fi ltering mechanism that accepts parameterizations only if they yield simultaneous agreement with observed data in several outputs of the model and a model with severe structural errors will fail to yield agreement in some of the model outputs (Martínez et al. 2011). If the observed data provide suffi cient information on system dynamics and the model shows no severe structural errors, the observed data constrain not only the model outputs but also the internal model functioning to produce reasonable behavior (Wiegand et al. 2004a). Under this assumption, we can study the internal model behavior to better understand the main processes governing the ecological system under study and use the model to make large-scale predictions.

In this study, we integrated the abundant fi eld data on the population dynamics and spatial organization of the

semiarid Patagonian grass-shrub steppe collected during the last 50 years into a spatially explicit and individual-based model. Th e vegetation model explicitly separates belowground and aboveground processes by including a previously developed soil water balance model (DINAQUA; Paruelo and Sala 1995). Soil water dynamics are the main limiting factor for the steppes. Th e ultimate goals of our model were to understand the role of diff erent plant pro-cesses on the long-term dynamics and spatial organization of vegetation in Patagonian grass–shrub steppes and to identify the most sensitive processes at the plant level that would allow us to detect degradation at early stages. How-ever, before this could be accomplished we needed toparameterize and test the model against multiple fi eld data. Th erefore, we focused on three specifi c tasks. In the fi rst step, we evaluated the ability of our model to gener-ate dynamics in accordance with detailed fi eld data and determined the values of unknown parameters using inverse parameterization techniques. In the second step, we per-formed a global sensitivity analyses to identify the main controls of vegetation with special emphasis on the shrub-grass balance. Finally, we characterized the emerging long-term dynamics for simulations that agreed with the available fi eld data.

Methods

Study area

Th e model was based on the semiarid grass-shrub steppe of the Occidental District of the Patagonian Phytogeographic Province (Le ó n et al. 1998). Th is vegetation district covers approximately 150 000 km 2 between the SubAndean and the Central District of Patagonia. Most of the information included in our model was obtained from the INTA Rio Mayo Experimental Field Station and neighboring ranches in Chubut, southwestern Patagonia (45 ° 41′S, 70 ° 16′W, 500 m a.s.l.), Argentina. Th e mean annual rainfall (MAP) at this site is 153 mm (n � 37, 1961 – 1998), ranging between 47 and 230 mm (driest and wettest year on record, respectively), and mostly (ca 73%) falling during the autumn and winter (March to September; Jobb á gy et al. 1995). Mean annual temperature is 8.4 ° C, with mean monthly temperature ranging between 2 ° C and 14 ° C, in July and January, respectively (Paruelo et al. 1998). Strong winds blow predominantly from west to east with high intensities. Soils have an upper sandy layer with 50% cob-bles and pebbles, and a cement-like stony layer (i.e. CO 3 Ca) at 0.45 – 0.6 m depth (Calciorthids, Paruelo et al. 1988).

Almost 50% of soil cover is bare ground and the rest is covered by tussock grasses (26 � 5% SE), shrubs (12 � 4%), and litter (5%) (Golluscio et al. 1982, Fern á ndez-Alduncin et al. 1991). Th e dominant tussock grass species are Stipa speciosa, S. humilis and Poa ligularis , whereas Bromus pictus is a sub-dominant bunch grass species. Th e Stipa spp. species are generally less palatable and have higher C:N ratios than P. ligularis and B. pictus (Semmartin et al. 2004). Th e dominant shrub species are Mulinum spinosum, Senecio fi laginoides and Adesmia volckmanni . Aboveground primaryproduction ranges between 10 and 120 g m �2 year �1

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(annual mean 56 g m �2 year �1 ; Jobb á gy and Sala 2000). Grasses and shrubs account for 53% and 43% of total aboveground net primary production [ANPP], respectively, while a heterogeneous group of forbs account for the rest.

Model overview

We tailored an individual-based, spatially-explicit model (DINVEG) to simulate the vegetation dynamics of the grass-shrub steppe. DINVEG simulates the spatial and temporal dynamics of the dominant grasses Stipa spp. , P. ligularis, B. pictus and the dominant shrubs M. spinosum, S. fi laginoides and A. volckmanni . Th ese species cover the main functional roles present in the steppe and can be thought of as plant functional types. In the simulation of vegetation dynamics, most processes were conditioned by soil water, the main limiting resource in this plant commu-nity. To describe the soil water dynamics, we integrated a previously developed soil water balance model (DINAQUA;Paruelo and Sala 1995) into DINVEG. To present DINVEG, we followed the standard ODD protocol for individual-based models suggested by Grimm et al. (2006). Th is protocol comprises three major blocks: overview, design concepts and details. In the following sections, we present the overview and design concepts. Th e details, rules and formulas used in the model are presented in the Supplementary material Appendix A1.

Purpose

Th e purpose of the modeling study was to understand the role of diff erent plant processes on the long-term dynamics and spatial organization of vegetation in arid ecosystems.

Scales

We simulated a 50 � 50 m steppe plot with a spatial resolution of 0.2 � 0.2 m (cell size). One cell corresponded to the approximate size of one grass tuft, but shrubs could occupy several cells. We selected this resolution to ade-quately represent the ecologically relevant processes (e.g. facilitation, competition, seed dispersal). In addition, the model simulated seven vertical layers and the seed soil bank. Th e fi rst layer represented the aboveground occupation by shrubs or grasses, and six 0.1 m thick belowground layers contained the root occupation and water dynamics in the soil layers (i.e. 0 – 0.1 m, 0.1 – 0.2 m, 0.2 – 0.3 m, 0.3 – 0.4 m,0.4 – 0.5 m, 0.5 – 0.6 m). Th is is the relevant scale for the soil characteristics, water dynamics, and root systems for the Occidental Patagonian steppes (Paruelo et al. 1988, Paruelo and Sala 1995). DINVEG uses a monthly time step, whereas DINAQUA uses a daily time step (Paruelo and Sala 1995). Th erefore, we integrated the daily information from DINAQUA to a monthly time step.

State variables

DINVEG comprises four types of objects: grass tufts, shrubs, the soil seed bank, and soil water. It simulates the spatial and temporal dynamics of the fi rst three objects, whereas soil water dynamics were modeled by DINAQUA

(see section ‘ Links between the vegetation dynamic and water balance models ’ ).

Grass tufts were characterized by an identity number, species ( Stipa spp. , P. ligularis or B. pictus ), location ( x, y coordinates), age, stage (i.e. seedling, adult, dead), above-ground plant biomass (g), and growth history (a record of individual growth during the last three years). According to sizes observed in the fi eld, grass tufts occupy only one cell in the model. Shrubs were additionally characterized by size (number of cells), and the area immediately adja-cent to the shrub in which shrubs may exert infl uence on grass seedlings (i.e. the grass ring or zone of infl uence) (Aguiar and Sala 1994). Based on observed shrub sizes, we allowed shrub size to vary between one and a maximum of 21 cells.

Th e soil seed bank records the number of viable seeds and seedlings per species for each cell. Soil water is estimated by DINAQUA for each cell at six diff erent depths as the volumetric soil water content. DINAQUA considers the grass and shrub biomass within the nine cell quadrat around the focal cell, as well as monthly radiation, daily precipi-tation and daily temperature data (see ‘ Links between the vegetation dynamic and water balance models ’ ).

Process overview and scheduling

For each individual, we simulated the main life history events of seed production, seed dispersal, plant growth, and mortality (Fig. 1). For non-occupied cells, we consid-ered seedling emergence and recruitment, and for all cells in the grid we simulated the soil seed bank dynamics (Fig. 1). Each life history event occurred during particular monthsaccording to the schedule observed in the fi eld. Because the Patagonian steppe is a water-limited ecosystem we assumed that the occurrence of the emergence and recruit-ment events depended on water content in specifi c soil lay-ers, and growth and seed production on plant transpiration (Fig. 1), both calculated by DINAQUA. Plant mortality was modeled with a species-specifi c annual mortality rate, which increased under water stress. Seed dispersal followed dispersal kernels parameterized from fi eld data that consid-ered the dominant wind direction. In the Supplementary material Appendix A1 (Model details) , we provide a detailed description of the diff erent rules and equations that govern the model dynamics in DINVEG.

Design concepts

Population and community dynamics emerge from the behavior of individual plants, and the life history of the diff erent species is represented by the empirical rules set. DINVEG describes three types of interactions between individuals: belowground water competition, aerial facilita-tion in the ring (i.e. shrub neighboring cells), and mortality of grass tufts in the ring if the shrub increases in size and overgrows grasses. Th e majority of model parameters were directly estimated from the literature or unpublished data (Supplementary material Appendix A1 Table A1). However, for uncertain parameters we used an inverse parameteriza-tion approach (Wiegand et al. 2003, 2004a, Hartig et al. 2011) based on data from several vegetation studies in the

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Seed Seedling Young

Adult

EmergenceEmergence Recruitment

Reproduction Mortality

Growth

Seed survivalSeed survival

Y

N

Y

Y

Y

Y

N

N

N

N

N

Growth

Seed dispersal

Y

Rule 1

Rule 2

Rules 3 & 4

Rules 5 & 6

Rules 7 & 8Rule 9

Fall & Winter water availability0–10 cm

Viability decay rate

Aerial facilitationSpring & Summer water availability 0–30 cm

Spatial competition

Water transpirationWater competition

Water competitionSpatial competition

Growth memoryAge

Water transpirationWater competition

Figure 1. Flow chart of the DINVEG model. Th e green boxes indicate the diff erent individual stages. Diamonds represent decision processes and rectangles are alternatives processes. Black thin solid arrows represent demographic transitions, whereas pink thick arrows represent the main controls for each process. Soil water content and transpiration control population process such emergence, recruitment, plant growth, mortality and reproduction.

study area (see section ‘ Model parameterization ’ ). We also conducted a local sensitivity analysis of main output vari-ables with respect to the model parameters.

Initialization

We constructed a 200-year rainfall and temperature time series by randomizing a record of 31 years of daily preci-pitation and temperature from the study area. A random-ization procedure was used to simulate climatic series that considered the observed autocorrelation between years as autoregressive models and conserved mean values and inter-annual variability (i.e. MAP � 153 mm year �1 and a

coeffi cient of variation CV �SDX

100⎡⎣⎢

⎤⎦⎥ of 33%).

Th e DINVEG rules rely heavily on inputs from the soil water balance model DINAQUA such as soil water content of the i th soil layer ( swc i ) or plant transpiration ( transp ) (Supplementary material Appendix A1 Table A1). However, direct coupling of DINAQUA and DINVEG by calling DINAQUA whenever a DINVEG rules requires an input would be computationally ineff ective. We there-fore used an alternative approach and generated a data bank that contained the monthly values of soil water content swc i and plant transpiration transp for all DINAQUA input parameters (such as ANPP) that may occur for the selected climatic series in this steppe. Whenever a DINVEG rules required an input DINAQUA it looked it up from the data bank. Th e data bank was created for a given climate time series for an array of 10 � 10 classes of grass and shrub ANPP ranging between 0 – 90 g m �2 year �1 (with a width of 10 g m �2 year �1 ). Th ese ANPP ranges are likely to occur in the Patagonian steppe (Jobb á gy and Sala 2000). Th e transformation of the continuous ANPP values into the

10 discrete classes caused a small approximation error. For example, under representative conditions the approxima-tion error yielded approximately 7% for the output variable transpiration. Th e approximation error was calculated as the mean of the absolute diff erences between the estimated transpiration based on exact ANPP values and that based on the corresponding discrete ANPP values, taken over a biomass range representative for the Patagonian steppes. Th en, this mean was expressed as percentage of the output model calculated with the exact inputs.

Input

Th e main input variables for DINVEG are provided by the soil water balance model DINAQUA that was devel-oped and calibrated for the Patagonian steppe (Paruelo and Sala 1995). Th e DINAQUA input used to simulate the soil water dynamics were organized in three blocks: climate, vegetation and soil. Climate input variables refer to monthly radiation, daily precipitation and daily tem-perature data which are provided by the climatic series. Vegetation input variables refer to ANPP of grasses and shrubs (simulated by DINVEG), root distribution in soil layers and transpiration parameters for each growth form (estimated for the steppe by Paruelo and Sala 1995). Soil input variables refer to the number of soil layers, their thick-ness, water content at fi eld capacity and water content at wilting point for each soil layer.

Links between the vegetation dynamic and water balance models

Th e vegetation model simulates the demographic processes ina cell using as input the soil water content and transpiration

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at our study site in a non-spatial way and a set of ‘ detailed ’ summary statistics (i.e. cover of high-cover patches, shrubsize structure, shrub aggregation, and grass-shrub asso-ciations) that quantifi ed detailed spatial patterns and size distributions of individual plants from the spatial organiza-tion of vegetation as two-phase mosaics (Table 1).

Th e basic summary statistics are given by average values (e.g. shrub cover, density or ANPP; Table 1). Because these data are subject to observation error and stochastic variability within the study site, we defi ned the match of the basic summary statistics based on conservatively wide ranges given by the observed mean � 2 SD (Table 1). Th e data were derived from fi eld observations at ungrazed sites that repre-sent the Occidental Patagonian steppes. Th is criterion works well if we assume that the system is near a stochastic equi-librium. Th is assumption is reasonable for these Patagonian steppes (Aguiar et al. 2005), but the presence of strong temporal trends (e.g. those induced by climate change) would complicate the inverse approach. For details on the acceptance ranges and fi eld studies see Table 1. Details on the criteria for matching basic and detailed summary statistics are provided in the Supplementary material Appendix A2, while the spatial pattern analyses are explained in Supplementary material Appendix A3.

Model parameterization

Th e DINVEG model contained a total of 17 parameters for each species group (Supplementary material Appendix A1 Table A2). Th e values of seven structural parameters for grasses (three species) and shrubs (three species) were esti-mated directly from published data or measured in the fi eld (Supplementary material Appendix A1), fi ve para-meters have been indirectly determined from published or unpublished data, and fi ve parameters that governed the life history events of emergence ( t e ), recruitment ( t r ), growth ( t tr ), reproduction ( t s ), and mortality ( p mk ) were unknown and therefore varied over their entire range.

that corresponds to the ANPP of grasses and shrubs in an area of 3 � 3 cells [i.e. the kernel of a moving window (0.6 � 0.6 m)] around the focal cell. We used the 3 � 3 cell neighborhood because the cell size used in DINVEG issmall in comparison to the area explored by roots. If the cell was vacant or occupied by a seedling, the processes simulated by DINVEG were emergence and recruitment and the DINAQUA-generated inputs were soil water content of the diff erent layers. If the cell contained an established plant, the processes were growth, seed production and mor-tality and the DINAQUA-generated inputs were transpira-tion of each growth form.

Model evaluation

Our approach is an inverse modeling technique that identi-fi es (from a large systematic sample of the parameter space) those parameterizations that yield agreement between model outputs and corresponding fi eld data (e.g. plant cover, species composition, spatial pattern) that are quan-tifi ed by summary statistics. Th is approach requires the following general steps: 1) the raw data is condensed into summary statistics to capture diff erent characteristic fea-tures of the steppe (Grimm et al. 2005, Komuro et al. 2006, Csill é ry et al. 2010, Hartig et al. 2011), 2) the match between the summary statistics calculated from simulated and observed data for a given parameterization and model are then quantifi ed, 3) a given model must then be para-meterized, and 4) if alternative models are formulated, the candidate model(s) most likely given the data is selected (Wiegand et al. 2003, 2004a).

Summary statistics and their observed ranges

We used ‘ basic ’ summary statistics (i.e. plant cover and plant density at life-form and species level, and ANPP at life-form level) that characterized the observed vegetation state

Table 1. Criteria and acceptance range for fi eld patterns fulfi llment against model outputs.

Summary statistic Acceptance range Bibliographic sources

Basic summary statistics Total cover 30 – 65% Aguiar et al. 2005, Fern á ndez-Alduncin et al. 1991,

Golluscio et al. 1982Grass cover 15 – 40%Shrub cover 5 – 20%Grass density 7 – 13 plants m �2 Aguiar et al. 2005, Rotundo and Aguiar 2005,

Oesterheld and Oyarz á bal 2004Density of Bromus 2 – 6 plants m �2 Density of Poa 2 – 4 plants m �2 Density of Stipa spp. 4 – 6 plants m� 2 Shrub density 0.3 – 1 plants m� 2 Cipriotti and Aguiar 2005, Cipriotti and Aguiar 2010Density of Mulinum 0.2 – 0.5 plants m �2 Density of Senecio 0.1 – 0.4 plants m �2 Density of Adesmia 0.05 – 0.3 plants m �2 Grass ANPP 10 – 49 g m �2 year �1 Fern á ndez-Alduncin et al. 1991, Jobb á gy and

Sala 2000Shrub ANPP 11.3 – 47.3 g m �2 year �1 Total ANPP 26.5 – 85.8 g m �2 year �1

Detailed summary statistics Cover of high-cover patches 18 – 38% Cipriotti and Aguiar 2005, Soriano et al. 1994Size-structure of shrubs no differences in the cumulative

frequency distributionsCipriotti and Aguiar 2010, O ñ atibia et al. 2010

Shrub aggregation signifi cant at 0.5 – 1 m Cipriotti and Aguiar 2010, Wiegand et al. 2006Grass – shrub association signifi cant at 0.1 – 0.7 m Cipriotti and Aguiar 2005, Wiegand et al. 2006

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and seed production because each threshold parameter triggered the occurrence of one key demographic event. Consequently, we can identify the more infl uential processes on long-term vegetation dynamics. We assumed that the most sensitive threshold parameter with respect to spe-cies density will point to a demographic constraint. Th is is because in this case a slightly lower threshold value will allow for more frequent occurrence of the associated demographic process and if this process was indeed limiting then the density of the respective species should greatly increase if the parameter value decreases. Th is will be noted by a steeper slope (and correlation) in the relationship between the threshold parameter and species abundance.

Results

Inverse model parameterization

Th e probability that total shrub or grass cover (or total shrub and grass density) matched individually for a given model parameterization was relatively high (Table 2). For example, total grass or shrub cover matched in 34.4% and 13.5% of all parameterizations, respectively. Total grass (or shrub) density matched in more than 40% of all parameter-izations, whereas grass and shrub ANPP matched in 24% of all parameterizations. Th ese results demonstrate that it was relatively easy for DINVEG to reproduce fi eld data of single variables (but note that we used conservatively wide acceptance ranges).

Results show, in general, a strong inverse relationship between shrub and grass cover (and density) because high shrub density was associated with low grass density and vice versa (Fig. 2). While the two basic density summary statistics individually matched in more than 40% of all parameterizations, we found that only 12.8% of all para-meterizations simultaneously matched shrub and grassdensity (Fig. 2, Table 2). Finally, simultaneous match in all species specifi c densities was only reached by 0.22% of all parameterizations, and when requiring an additional match in ANPP, this fi gure was further reduced to 0.05% (i.e. 5 parameterizations; Table 2).

We used a hierarchical approach for estimation of the 30 parameters that were unknown and demanded fi rst that the set of basic summary statistics describing plant cover, density and ANPP (Table 1) were met. In a second step, we compared the model outputs generated by the para-meterizations that passed the criteria of the fi rst step with the set of detailed summary statistics that were related with spatial structure. We can regard the fi rst step as model fi tting and the second step as validation because it uses independent data.

To estimate the values of the unknown parameters, we used an inverse approach similar to that described in Wiegand et al. (2004a). We systematically sampled the entire parameter space using a Latin hypercube design (Stein 1987), a stratifi ed sampling method without replacement. Th e Latin hypercube results in equal prob-abilities for each parameter corresponding to uninforma-tive priors in a Bayesian framework. For each unknown parameter, we selected an interval within which the para-meter was varied (i.e. lower and upper limits) and divided it into 10 equidistant subintervals. We generated a total of 10 000 model parameterizations. Note that this approach estimates the unknown parameters conditionally on the cur-rent knowledge of the other parameters (and the assumed model structure), assuming no uncertainty in their values. To test this assumption we also conducted model para-meterizations where all parameters were varied within their observed ranges and following their probability density function (when this information was available from biblio-graphy or fi eld data), instead of being fi xed to their most likely value.

For each parameterization a DINVEG simulation was run for 200 years. All simulations were initialized with the same vegetation plot that represented Patagonian grass-shrub steppes in good condition (i.e. not degraded) under a typical climate series (i.e. MAP � 153 mm year �1 ;CV � 33%). We then compared the mean of the summary statistics (i.e. calculated from the last 100 years and the whole plot) with the ranges calculated from the fi eld obser-vations and determined whether or not it was matched (Table 1). Only parameterizations for which the simulated data produced simultaneous match in all summary statistics were accepted.

Sensitivity analyses

We evaluated the sensitivity of the model at two levels of biological organization (growth-form and species) by calcu-lating multiple backward stepwise regression analyses and Spearman rank correlation coeffi cients between a model output variable and a parameter. We studied the response in the average ANPP of grasses and shrubs, and grass, shrub and species-specifi c densities to changes in the four soil water content or transpiration thresholds t e , t r , t tr and t s , and the mortality rate p mk . We conducted a global sensitivity analysis (Wiegand et al. 2004a) by using all 10 000 model parameterizations for the multiple regressions and correla-tion analyses.

Th e sensitivity analyses allowed us to explore potential demographic constraints in emergence, recruitment, growth,

Table 2. Summary of the inverse parameter estimation for DINVEG model based on the basic patterns. Numbers indicate the percent-age of parameterizations for which the simulated output variables was within the observed fi eld range.

Basic pattern Acceptance (%)

Total grass cover 34.3Total shrub cover 13.5Total grass and total shrub cover 12.8

Total grass density 43.2Total shrub density 41.1Total grass and total shrub density 12.8

Species specifi c grass densities 9.9Species specifi c shrub densities 2.1Species specifi c grass and shrub densities 0.22

ANPP 24.4All basic patterns 0.05

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in the fi eld (Cipriotti and Aguiar 2010). We also found that positive spatial associations between simulated grasses andshrubs occurred at short distances ( � 0.7 m; Fig. 4d), as has been commonly reported for these grass-shrub steppes (Cipriotti and Aguiar 2005).

Although we had no long-term data on life form or species-specifi c densities to contrast against the model out-puts, the inter-annual variability of the time series of plant species density and net productivity simulated by DINVEG was well within the envelopes (mean � 2 SD) from fi eld data of grazing-excluded plots (Fig. 5). Equilibrium condi-tions were reached after approximately 25 years for all plant species in density and net productivity dynamics (Fig. 5).

Sensitivity analysis

Grass density was strongly correlated with the recruitment thresholds of the three grass species and weakly correlated with the emergence thresholds of Adesmia and Bromus (Table 3A). Th e correlation of grass density with grass recruitment thresholds was negative because a high recruit-ment threshold means fewer opportunities for recruitment and hence less recruitment of grass seedlings. However, the correlation with emergence thresholds of shrubs were posi-tive because higher thresholds mean lower shrub density and therefore higher grass density. Shrub density showed overall weaker correlations, but with more parameters, indicating more complex interactions. Total shrub density was negatively correlated with shrub emergence and recruit-ment thresholds, and positively with the recruitment thresh-olds of all three grasses (Table 3F). Total grass and shrub ANPP were correlated with recruitment and emergence threshold parameters, but additionally with maximum plant growth and growth threshold parameters (Table 3B, G). Regression analyses showed that shrub ANPP was poorly explained by model parameters (R 2 � 0.39, p � 0.001), whereas grass density, grass ANPP and shrub density were better explained (R 2 � 0.87 � 0.88, p � 0.001). Finally, the slope values of the multiple regression analysis agreed well with the respective correlation coeffi cients. Th is indicates that a strong correlation between an output variable and a parameter translated in our case into a large sensitivity of the output variables to the demographic parameters (Table 3).

Model validation with detailed summary statistics

All fi ve parameterizations of the model that matched the basic summary statistics also matched the detailed sum-mary statistics. Th e mean aerial cover of high cover patches of the mosaic (i.e. shrubs surrounded by a dense grass ring) simulated by DINVEG (23%) was well within the 95% prediction envelope (18 – 38%) reported for ungrazed con-ditions (Cipriotti and Aguiar 2005). In addition, the size structure based on shrub biomass simulated by DINVEG agreed well with the variation observed in the fi eld (Fig. 3; Cipriotti and Aguiar 2010, O ñ atibia et al. 2010).

Th e spatial patterns of the simulated vegetation at year 200 (Fig. 4a, c) were also in good agreement with that observed on the steppe. Figure 4 shows an example for one simulation with a parameterization that matched all fi eld data simultaneously. Shrubs showed an aggregation at short distances ( � 1 m; Fig. 4b) similar to that observed

Figure 2. Relationships between (a) shrub and grass cover and (b) shrub and grass density simulated by DINVEG during 200 years for the whole set of parameters used during the calibration. Dotted lines indicate the fi eld abundance range for both growth-forms (mean � 2SD) and the box the parameterizations with match in both patterns. Percentages indicate the relative number of simula-tions fallen within the fi eld range.

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Figure 3. Relative cumulative frequency of biomass distribution of shrubs from fi eld (gray circles) and simulated data. Gray dashed lines indicate the prediction envelope (95%) from the logarithmic function fi tted to the fi eld data.

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Figure 4. Summary of the spatial structure of the two-phase mosaic simulated by DINVEG after 200 years for the calibrated parameters and a typical climate series and a representative vegetation origin from the grass-shrub Patagonian steppe. Vegetation maps (50 � 50 m) for: (a) the two main life forms, and (c) the six dominant plant species. (b) Relative univariate O -ring statistic for the spatial aggregation of shrubs. (d) Relative bivariate O -ring statistic for the grass-shrub associations. Dashed lines indicate the simulation envelopes (95%) for CSR of shrubs (b) or the null model with CSR for grass tufts and fi xed shrubs (d). Insets in panels ‘ b ’ and ‘ d ’ quantify the respective spatial patterns from fi eld surveys.

As expected, threshold parameters of individual spe-cies were the strongest determinants of its own density (Table 3C – E, H – J). Again, density of a given grass species correlated most strongly with its own recruitment thresh-old (Table 3C – E), whereas the density of a given shrub species correlated strongly with its emergence threshold (Table 3H – J). Th us, the most important demographic con-straint for grasses is the recruitment phase (Fig. 6a), whereas the most important demographic constraint for shrubs is emergence (Fig. 6b). However, for individual shrub species we found interspecifi c interactions with grass recruitment thresholds (Table 3H – J), whereas grass density was not strongly correlated with shrub parameters (Table 3C – E). For example, the abundances for all shrub species showedpositive correlations with grass recruitment thresholds of Poa and Stipa species (0.21 � r SP � 0.27; p � 0.001), indi-cating that grass density controlled shrub density. Interest-ingly, the other parameters governing mortality, growth and reproduction showed a generally low sensitivity to the model output variables analyzed (Table 3).

We assumed that uncertainty in the fi ve parameters (per species) estimated from published or unpublished data can be neglected in a fi rst approximation. To test this assump-tion we conducted model simulation where we allowed these parameters to change within their observed ranges. We found that model predictions were generally in agreement with that of our main parameterization. Th e results of the sensitivity analysis identifi ed emergence and recruitment parameters as the most infl uential parameters on response variables such as plant cover, density and ANPP (results not shown).

Dynamics of the Patagonian grass-shrub steppe

We used the data generated by the model simulations of the fi ve parameterizations that produced a match of all summary statistics to explore the dynamics shown by the model. Th e dynamics can be characterized as a stochas-tic equilibrium with considerable inter-annual variability. While the coeffi cient of variation of the input rainfall data was 33%, the variability of total shrub density was lower (CV � 19%), and that of grass density was considerably lower (CV � 9%). Variability in ANPP was somewhat between that of grasses and shrubs (CV � 16%). Th us, ecosystem function buff ered environmental fl uctuations.

Th e simulated ANPP was moderately explained by a second order polynomial regression (Fig. 7) with the pre-cipitation in the warm period of the current year and the total precipitation in the previous year as the main predic-tors ( r 2 � 0.27, p � 0.001). All second order terms in the regression analysis were signifi cant, but the estimated eff ects diff ered in the sign of the coeffi cients. While the quadratic coeffi cient of the annual previous precipitation was negative, the quadratic coeffi cient of precipitation in the warm period was positive and one order of magnitude higher, pointing to diff erences in the slope changes.

Total grass and shrub densities for each simulation were highly correlated along years ( r � 0.69, p � 0.001), point-ing to a common driver. We explored the underlying reason for this high correlation by regressing the density ( N t ) and population growth rates (i.e. Nt0

� Nt�1/t0 � t�1) for each

focal species against the main environmental input variables

856

variables than Mulinum and Senecio (0.43 � r � 0.53, p � 0.01) and the environmental controls were weaker and less signifi cant in explaining plant density or population growth rate ( r 2 � 0.1 – 0.17, β � 0.3, p � 0.03).

For the three grass species, we found that the environ-mental variables explained the population growth rate better (0.58 � r 2 � 0.68, p � 0.01) than plant density (0.2 � r 2 � 0.35, p � 0.01). Two strong environmental driv-ers were common to the three grass species: the current soil water content in the top layer (0 – 10 cm) during the emer-gence period ( β � 0.57 – 0.62, p � 0.001) and the current soil water content in the intermediate layers (10 – 30 cm) during the recruitment period ( β � 0.2 – 0.36, p � 0.001).

Discussion

In this study, we tackled a persistent problem in model parameterization in spatially-explicit and individual-based simulation modeling, which has hindered wider application of these types of models (Wiegand et al. 2004a, Grimm and Railsback 2005). Analysis of mecha nistically-rich simulation models requires considerable eff ort (DeAngelis and Mooij 2003, Wiegand et al. 2003, Grimm and Railsback 2005). Th is is because the diff erent mecha-nisms are often governed by many model para meters (our six species model had a total of 17 � 6 � 102 para-meters), and even in systems that are well stu died (as for example the Patagonian steppes), not all model para-meters can be directly determined from fi eld data (12 � 6 � 72 parameters were based on fi eld data). Uncertainty in model parameters, error propagation, and lack of rigorous methods of model selection have been the major points of criticism against mechanistically-rich, individual-based and spatially-explicit simulation models (DeAngelis and Mooij 2003, Wiegand et al. 2004a, Grimm and Railsback 2005, Martínez et al. 2011).

Our approach took advantage of the ability of individual-based models to generate outputs at larger scales that can be compared with fi eld observations (Grimm et al. 2005). In many applied problems, such as degradation in semiarid rangelands, there are usually not the time and resources available to conduct detailed fi eld studies that would allow for direct parameterization of the model. However, larger scale data such as community composition and abundances are routinely collected. We demonstrated in this study that such data are a valuable source of information that can be used for inverse parameterization (see also Wiegand et al. 2004a) and assessment of long-term community dynamics.

Th e inverse pattern oriented approach presented here parallels recent developments in Approximate Bayesian computation (ABC) used especially in evolutionary genet-ics (Csill é ry et al. 2010, Hartig et al. 2011). Similar to our approach, ABC bypasses exact likelihood calculations by using summary statistics and simulations. Our approach of model fi tting is analogous to the rejection fi lter approach, which is one of three major ABC algorithms for model fi tting (Beaumont et al. 2002, Hartig et al. 2011). Model parameterizations are generated from a probability distri-bution. Th e data generated by model simulation are then reduced to summary statistics, and the sampled parameters

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Figure 5. Time series of (a) grass species density, (b) shrub species density, and (c) total annual net primary productivity (ANPP) simulated by DINVEG during 200 years for calibrated para-meters in a plot of 1/4 ha. Th in vertical bars indicate envelopes (mean � 2 SD) for fi eld species density data and ANPP of grazing excluded paddocks from Patagonia. Deviation from fi eld data represents spatio-temporal variability.

(i.e. precipitation and the water content for diff erent soil layers) for the current and previous years ( t 0 , t � 1 or t � 2 ), considering two main seasons (i.e. cold [emergence] or warm [recruitment] season). Generally, the environmen-tal variables that were signifi cantly related to plant density (or population growth rate) were diff erent among grass and shrub species.

For the shrub species Mulinum and Senecio , the strongest control of plant density and population growth rate was the current soil water content in the top layer (0 – 10 cm) during the emergence period ( r 2 � 0.3 – 0.42, β � 0.47 – 0.5, p � 0.001). Th is also explained the synchronous short-term fl uctuations between both species ( r � 0.89, p � 0.001; Fig. 5b). However, the density and population growth rate of Adesmia showed weaker correlations with environmental

857

Table 3. Spearman rank correlation ( r SP ) and slope ( β 1 ) coeffi cients between model parameters and growth-form or species density and ANPP calculated for all 10 000 parameterizations of the DINVEG model. Shown are the largest slopes and correlations for each species and growth form (p � 0.001) in descending order.

Prediction Parameters r SP β 1

(A) Total grass density Stipa recruitment threshold �0.44 �0.43 Poa recruitment threshold �0.44 �0.42 Bromus recruitment threshold �0.39 �0.4 Adesmia emergence threshold 0.25 0.23 Mulinum emergence threshold 0.19 0.21

(B) Total grass ANPP Poa recruitment threshold �0.36 �0.35 Stipa recruitment threshold �0.36 �0.36 Bromus recruitment threshold �0.34 �0.33 Mulinum emergence threshold 0.27 0.28 Poa max plant growth 0.21 0.19 Stipa max plant growth 0.19 0.19

(C) Mean Bromus density Bromus recruitment threshold �0.84 �0.81 Bromus emergence threshold �0.31 �0.33 Bromus mortality rate �0.25 �0.26

(D) Mean Poa density Poa recruitment threshold �0.85 �0.82 Poa emergence threshold �0.32 �0.34 Poa mortality rate �0.19 �0.2

(E) Mean Stipa density Stipa recruitment threshold �0.85 �0.81 Stipa emergence threshold �0.33 �0.33 Stipa mortality rate �0.19 �0.19

(F) Total shrub density Adesmia emergence threshold �0.35 �0.32 Stipa recruitment threshold 0.34 0.32 Mulinum emergence threshold �0.3 �0.31 Poa recruitment threshold 0.33 0.3 Bromus recruitment threshold 0.28 0.29 Senecio emergence threshold �0.28 �0.28 Mulinum recruitment threshold �0.24 �0.25 Senecio recruitment threshold �0.23 �0.23 Adesmia recruitment threshold �0.22 �0.22

(G) Total shrub ANPP Mulinum emergence threshold �0.25 �0.28 Mulinum growth threshold �0.21 �0.25 Mulinum recruitment threshold �0.19 �0.22 Senecio growth threshold �0.16 �0.17 Senecio emergence threshold �0.17 �0.16 Stipa recruitment threshold 0.17 0.16 Poa recruitment threshold 0.15 0.16 Mulinum mortality rate �0.12 �0.14

(H) Mean Mulinum density Mulinum emergence threshold �0.68 �0.66 Mulinum recruitment threshold �0.47 �0.5 Mulinum mortality rate �0.21 �0.22 Stipa recruitment threshold 0.21 0.21 Poa recruitment threshold 0.23 0.2

(I) Mean Adesmia density Adesmia emergence threshold �0.67 �0.64 Adesmia recruitment threshold �0.4 �0.41 Adesmia mortality rate �0.25 �0.26 Stipa recruitment threshold 0.27 0.25 Poa recruitment threshold 0.25 0.23 Bromus recruitment threshold 0.22 0.21

(J) Mean Senecio density Senecio emergence threshold �0.7 �0.66 Senecio recruitment threshold �0.5 �0.5 Stipa recruitment threshold 0.22 0.22 Poa recruitment threshold 0.22 0.21 Bromus recruitment threshold 0.18 0.2

are accepted or rejected on the basis of the distance between the simulated and the observed summary statistics. Th e subsample of accepted values contains the fi tted parameter values, and allows evaluation of the uncertainty in para-meters given the observed statistics (Csill é ry et al. 2010) and prior fi eld data included in the model structure and parameterization.

However, in contrast to the rejection approach in ABC, we converted the distance between the simulated and the observed summary statistics into a binary measure of model fi t for each summary statistic. Binary measures of model fi t have also been advocated by others (Reynolds and Ford 1999, Komuro et al. 2006). Th e reason for using binary measures is that observations are subject to errors

858

that produced model outputs that were clearly unrealistic. However, all summary statistics taken together consider-ably constrained the parameter space and model behavior (see also Wiegand et al. 2004a for a detailed discussion of this issue).

Clearly, a valid parameterization had to balance the dif-ferent demographic processes correctly to yield the observed ANPP, species-specifi c cover and densities. Only few para-meterizations were able to do so. However, the fact that our model was able to match multiple fi eld observations

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Figure 6. Annual population growth of grasses (a) and shrubs (b) related to the average soil water content during the recruitment phase (October – December) in the fi rst two soil layers (0 – 20 cm) and the emergence phase (July – September) in the top soil layer (0 – 10 cm), respectively. Both data were built from a 200 year simulation with calibrated parameters. Dashed lines indicate the lower and upper limits of 95% confi dence envelopes from the respective fi ts.

Figure 7. Polynomial relationship between the total ANPP simulated by DINVEG with the calibrated parameters and the current precipitation during the warm period (P w ) and the immediate previous annual precipitation (P t�1 ) for a representative initial vegetation condition and a typical climate series. Th e 2nd order polynomial function is ANPP � 17.24 � 0.42 P t�1 � 0.16 P w � 0.0008 P t�1 2 � 0.0025 P w 2 � 0.0017 P t�1 P w (r 2 � 0.27, p � 0.001). Circles are the simulated data by DINVEG.

and inherent stochasticity that needs to be considered. Our approach would be able, in theory, to minimize the distance between the simulated and the observed summary statistics, but diff erentiating parameterizations with dis-tances below the level of uncertainty does not seem neces-sary. Doing so may cause bias or overfi tting (Wiegand et al. 2003, 2004a, Latombe et al. 2011). In our study we usedconservative, wide acceptance ranges for the summary statistics. With this, we aimed to exclude, based on each individual summary statistics, only model parameterizations

859

grounded in diff erent modeling philosophies and assump-tions. Th e matrix is usually deterministic (i.e. no changesof transitions or fecundities with time) and density-independent (i.e. the transitions or fecundities do not depend on plant density). However, our model allowed tran-sitions among plant stages to change in response to annualrainfall (which introduced a considerable stochasticity typical for event-driven semiarid systems) and intra- and inter-specifi c interactions (e.g. water competition, aerial facilita-tion or space competition) were density-dependent.

Interestingly, grasses controlled the shrub demography. Th is result is probably caused by water competition in the upper soil layers exerted by grasses (especially adults) on the early life stages of shrubs (e.g. seedlings or recruiters). Th e fi rst two years after their emergence, the roots of shrubs are constrained to the upper soil layers (0 – 10, 10 – 20 or 20 – 30 cm depending on time since emergence) and share water resources with grasses (i.e. rules no. 2, 3 and 6 from Supplementary material Appendix A1). Th is temporal resource overlap between shrubs and grasses generates an eff ective control for shrubs. Because the soil water content during emergence and recruitment is the key demographic process for grasses, they are mostly self-controlled (i.e. the higher water effi cient species) and spatial competition with shrubs can be neglected, except for M. spinosum where it plays only a minor role (see rule no. 7 from Supplementary material Appendix A1).

Th e dynamic aspects of ecosystem functioning simulated by DINVEG were in good agreement with fi eld observa-tions from these Patagonian steppes. For example, the inter-annual variability of total ANPP simulated by DINVEG (CV � 16%) was within the range estimated for our study site (15 – 27%). Th is result confi rms results from a fi eld study by Paruelo et al. (2000) that suggested that biotic constrains in ecosystem functioning buff er the high environmental variability in rainfall (i.e. CV � 33%). Th e moderate pre-dictive power of the relationships between simulated ANPP and annual or seasonal rainfall ( r 2 � 0.2 – 0.4, p � 0.01) were also in agreement with fi eld studies and point to biotic constrains on ANPP that contribute to diff erences between the spatial and temporal models of ANPP (Lauenroth and Sala 1992, Yahdjian and Sala 2006). In addition, the time lags of ANPP responses agree with memory eff ects reported in semiarid grasslands (Oesterheld et al. 2001, Wiegand et al. 2004b, Bartelt-Ryser et al. 2005) and/or the slow dynamics of water drainage and the shrub responses related to this water source (Golluscio et al. 1998, Jobb á gy and Sala 2000, Paruelo et al. 2000).

Conclusions

We showed that inverse parameterization of individual-based and spatially-explicit simulation models allows for an integration of short-term data on individual plant behav-ior with larger scale patterns that are routinely collected. Our approach allowed us to identify the key ecological processes that control long-term vegetation dynamics and to ‘ reconstruct ’ important characteristics of long-term com-munity dynamics. For the Patagonian steppes, seedling emergence and recruitment are critical processes for long-term vegetation dynamics. While sheep grazing is known to

is important because it shows that the model structure is consistent with the current data on the Patagonian steppe. In contrast, a model with missing or incorrectly specifi ed mechanisms would fail to match some of the observed data (Martínez et al. 2011) and subsequent modeling cycles are required to identify the missing or incorrectly speci-fi ed mechanisms (Wiegand et al. 2003). Th e weak impact of the variability of ‘ fi xed ’ parameters on model results can be explained by the narrow ranges of the ‘ fi xed ’ parameters compared to the unknown parameters that were varied over their entire range. In addition, this type of inverse para-meterization is not prone to error propagation (Wiegand et al. 2003). Th is could also contribute to the reduced impact of ‘ fi xed ’ parameters on model results.

Th e detailed summary statistics evaluate aspects of spa-tial structure that are substantially diff erent from the com-positional features tested by the basic summary statistics. We asked if the basic summary statistics were already able to constrain the model behavior suffi ciently to generate spatial structures that match the corresponding fi eld obser-vations. Interestingly, we found that model parameteriza-tions that matched the basic summary statistics (Table 1) generated the observed two-phase mosaic pattern where high-cover patches (co-dominated by shrubs surrounded by a dense grass ring) are interspersed in a low cover and grass-dominated matrix (Cipriotti and Aguiar 2005). Th is con-frontation of the fi tted model with detailed data on spatial structure can be regarded as model validation. Th us, given that the overall model structure does not contain severe structural errors, routinely collected compositional data can provided suffi cient information to constrain the internal model behavior in a way that even subtle spatial patterns were correctly predicted.

Dynamics of the Patagonian grass-shrub steppe

Our sensitivity analyses considered ‘ fast ’ variables such as plant density as well as a ‘ slow ’ variables (e.g. cover). Th e results for grass and shrub ANPP and density agreed with previous long-term fi eld studies on woody or perennialgrass species from semi-arid ecosystems (Milton 1995, Watson et al. 1997, Fair et al. 1999) where regeneration (i.e. emergence and recruitment) was the most important demographic process for the maintenance of plant popula-tions. Interestingly, recruitment and emergence parameters were signifi cantly correlated with slow and fast variables (Table 3). Th us, the shrub-grass balance and long-term veg-etation dynamics can be strongly modifi ed by environmental variables that aff ect recruitment and emergence. We found that the soil water content in the upper (0 – 10 cm) and intermediate soil layers (10 – 30 cm) at the end of the grow-ing season was especially important for this, given that seed availability is not constrained (Aguiar et al. 1992, Rotundo and Aguiar 2005, Cipriotti et al. 2008).

Our fi nding that recruitment and emergence parameters were the most sensitive parameters with respect to long-term population growth rates contrasts with results typically derived from matrix models for woody species where the stasis (i.e. survival) is generally the most sensitive demo-graphic parameter (Silvertown et al. 1993, Franco and Silvertown 2004). Th e reason for this diff erence may be

860

Fair, J. et al. 1999. Demography of Bouteloua gracilis in a mixed prairie: analysis of genets and individuals. – J. Ecol. 87: 233 – 243.

Fern á ndez-Alduncin, R. J. et al. 1991. Woody and herbaceous aboveground production of a Patagonian steppe. – J. Range Manage. 44: 434 – 437.

Franco, M. and Silvertown, J. 2004. A comparative demography of plants based upon elasticities of vital rates. – Ecology 85: 531 – 538.

Gian-Reto, W. et al. 2002. Ecological responses to recent climate change. – Nature 416: 389 – 395.

Golluscio, R. A. et al. 1982. Caracterizaci ó n fi tosociol ó gica de la estepa del oeste de Chubut, su relaci ó n con el gradiente ambiental. – Bol. Soc. Argentina Bot. 21: 299 – 324.

Golluscio, R. A. et al. 1998. Diff erential use of large summer rainfall events by shrubs and grasses: a manipulative experi-ment in the Patagonian steppe. – Oecologia 115: 17 – 25.

Grimm, V. and Railsback, S. F. 2005. Individual-based modeling and ecology. – Princeton Univ. Press.

Grimm, V. et al. 2005. Pattern-oriented modeling of agent-based complex systems: lessons from ecology. – Science 311: 987 – 991.

Grimm, V. et al. 2006. A standard protocol for describing individual-based and agent-based models. – Ecol. Modell. 198: 115 – 126.

Hartig, F. J. et al. 2011. Statistical inference for stochastic simulations models – theory and application. – Ecol. Lett. 14: 816 – 827.

Jackson, R. B. et al. 2000. Belowground consequences of vegeta-tion change and their treatment in models. – Ecol. Appl. 10: 470 – 483.

Jeltsch, F. et al. 2000. Ecological buff ering mechanisms in savannas: a unifying theory of long-term tree-grass coexistence. – Plant Ecol. 161: 161 – 171.

Jobb á gy, E. and Sala, O. E. 2000. Controls of grass and shrub aboveground production in the Patagonian steppe. – Ecol. Appl. 10: 541 – 549.

Jobb á gy, E. G. et al. 1995. Estimaci ó n del r é gimen de precipitaci ó n a partir de la distancia a la cordillera en el noroeste de la Patagonia. – Ecol. Austral 5: 47 – 53.

Komuro, R. et al. 2006. Th e use of multi-criteria assessment in developing a process model. – Ecol. Modell. 197: 320 – 330.

Kramer-Schadt, J. et al. 2007. Patterns for parameters in simulation models. – Ecol. Modell. 204: 553–556.

Latombe, G. et al. 2011. Levels of emergence in individual based models: coping with scarcity of data and pattern redundancy. – Ecol. Modell. 222: 1557 – 1568.

Lauenroth, W. K. and Sala, O. E. 1992. Long-term forage pro-duction of North American shortgrass steppe. – Ecol. Appl. 4: 397–403.

Le ó n, R. J. C. et al. 1998. Grandes unidades de vegetaci ó n de la Patagonia extra andina. – Ecol. Austral 8: 125 – 144.

Levin, S. A. 1992. Th e problem of pattern and scale in ecology. – Ecology 73: 1943 – 1967.

Mart í nez, I. et al. 2011. Disentangling the formation of contrasting tree-line physiognomies combining model selection and Bayesian parameterization for simulation models. – Am. Nat. 177: E136 – E152.

Milton, S. J. 1995. Spatial and temporal patterns in the emergence and survival of seedlings in arid Karoo shrubland. – J. Appl. Ecol. 32: 145 – 156.

Oesterheld, M. and Oyarz á bal, M. 2004. Grass-to-grass protection from grazing in a semi-arid steppe. Facilitation, competition, and mass eff ect. – Oikos 107: 576 – 582.

Oesterheld, M. et al. 2001. Interannual variation in primary production of a semi-arid grassland related to previous-year production. – J. Veg. Sci. 12: 137 – 142.

infl uence these processes, our study shows that the predicted increase of dry years (Gian-Reto et al. 2002) is likely to play an increasing role in controlling emergence and recruitment of both grass and shrub species (Cipriotti and Aguiar 2010).

Acknowledgements – We thank all fi eld ecologists from diff erent research institutions (CONICET, INTA, CIC, Universities, etc.) for their contribution to obtain data on the Patagonian steppe that nurtured our modeling and synthesis approach. We thank Dr. Peter Adler for key comments that improved the original manuscript. We also thank INTA and local ranchers for granting us access to their fi elds for scientifi c research. Th e studies reported in this manuscript comply with the ethics guidelines and current laws of the Republic of Argentina. Th is work was supported by grants from the Alexander von Humboldt-Stiftung, DAAD, Deutsche Forschungsgemeinschaft (DFG), Fundaci ó n Antorchas, Agencia Nacional de Promoci ó n Cient í fi ca y Tecnol ó gica (PICT 00462), Consejo Nacional de Investigaciones Cient í fi cas y Tecnol ó gicas (PIP 5963/05), and Univ. de Buenos Aires. PAC was supported by a doctoral fellowship from CONICET and a post-doc Georg Forster fellowship from the Alexander von Humboldt Foundation. TW and PAC were supported by the ERC advanced grant 233066.

References

Aguiar, M. R. and Sala, O. E. 1994. Competition, facilitation, seed distribution, and the origin of patches in a Patagonian steppe. – Oikos 70: 26 – 34.

Aguiar, M. R. et al. 1992. Competition and facilitation in the recruitment of seedlings in the Patagonian steppe. – Funct. Ecol. 6: 66 – 70.

Aguiar, M. R. et al. 2005. Procesos poblacionales denso-dependientes y la generaci ó n de patrones de heterogeneidad dentro de la comunidad. – In: Oesterheld, M. et al. (eds), La heterogeneidad de la vegetaci ó n de los agroecosistemas. Un homenaje a Rolando Le ó n. Editorial Facultad de Agronom í a-UBA, pp. 59 – 79.

Bartelt-Ryser, J. et al. 2005. Soil feedbacks of plant diversity on soil microbial communities and subsequent plant growth. – Persp. Plant Ecol. Evol. Syst. 7: 27–49.

Beaumont, M. A. et al. 2002. Approximate Bayesian computation in population genetics. – Genetics 162: 2025 – 2035.

Briske, D. D. et al. 2003. Vegetation dynamics on rangelands: a critique of the current paradigms. – J. Appl. Ecol. 40: 601–614.

Burnham, K. P. and Anderson, D. R. 2002. Model selection and multimodel inference: a practical information-theoretic approach, 2nd ed. – Springer.

Cipriotti, P. A. and Aguiar, M. R. 2005. Eff ects of grazing on patch structure in a semi-arid two-phase vegetation mosaic. – J. Veg. Sci. 16: 57 – 66.

Cipriotti, P. A. and Aguiar, M. R. 2010. Resource partitioning and interactions enable coexistence in a grass-shrub steppe. – J. Arid Environ. 74: 1111 – 1120.

Cipriotti, P. A. et al. 2008. Does drought control emergence and survival of grass seedlings in semi-arid rangelands? An example with a Patagonian species. – J. Arid Environ. 72: 162 – 174.

Csill é ry, K. et al. 2010. Approximate Bayesian computation (ABC) in practice. – Trends Ecol. Evol. 25: 410 – 418.

DeAngelis, D. L. and Mooij, W. M. 2003. In praise of mechanis-tically-rich models. – In: Canham, C. D. et al. (eds), Models in ecosystem science. Princeton Univ. Press, pp. 63 – 82.

861

Silvertown, J. et al. 1993. Comparative plant demography – relative importance of life-cycle components to the fi nite rate of increase in woody and herbaceous perennials. – J. Ecol. 81: 465 – 476.

Sharp, B. R. and Whittaker, R. J. 2003. Th e irreversible cattle-driven transformation of a seasonally fl ooded Australian savanna. – J. Biogeogr. 30: 783 – 802.

Soriano, A. et al. 1994. Patch structure and dynamics in a Patago-nian arid steppe. – Vegetatio 111: 127 – 135.

Stein, M. 1987. Large sample properties of simulations using Latin hypercube sampling. – Technometrics 29: 143 – 151.

Tietjen, B. and Jeltsch, F. 2007. Semi-arid grazing systems and climate change: a survey of present modelling potential and future needs. – J. Appl. Ecol. 44: 425 – 434.

Watson, I. W. et al. 1997. Demography of two shrub species from an arid grazed ecosystem in Western Australia 1983 – 1993. – J. Ecol. 85: 815 – 832.

Wiegand, T. et al. 1995. A simulation model for a shrub-ecosystem in the semi-arid Karoo, South Africa. – Ecology 76: 2205 – 2221.

Wiegand, T. et al. 2003. Using pattern-oriented modeling for revealing hidden information: a key for reconciling ecological theory and application. – Oikos 100: 209 – 222.

Wiegand, T. et al. 2004a. Reducing uncertainty in spatially explicit population models. – Biodivers. Conserv. 13: 53 – 78.

Wiegand, T. et al. 2004b. Do grasslands have a memory: modeling phytomass production of a semiarid South African grassland. – Ecosystems 7: 243 – 258.

Wiegand, T. et al. 2006. Extending point pattern analysis for objects of fi nite size and irregular shape. – J. Ecol. 94: 825 – 837.

Wood, S. N. 2010. Statistical inference for noisy nonlinear ecological dy\namic 792 systems. – Nature 466: 1102 – 1104.

Yahdjian, L. and Sala, O. E. 2006. Vegetation structure con-strains primary production response to increased water avail-ability in the Patagonian steppe of Argentina. – Ecology 87: 952 – 962.

O ñ atibia, G. R. et al. 2010. Individual plant and population biomass of dominant shrubs in Patagonian grazed fi elds. – Ecol. Austral 20: 269 – 279.

Paruelo, J. M. and Sala, O. E. 1995. Water losses in the Patagonian steppe: a modelling approach. – Ecology 76: 510 – 520.

Paruelo, J. M. et al. 1988. Soil water availability in the Patagonian arid steppe: gravel content eff ect. – Arid Soil Res. Rehab. 2: 67 – 74.

Paruelo, J. M. et al. 1998. Th e climate of Patagonia: general patterns and controls on biotic processes. – Ecol. Austral 8: 85 – 101.

Paruelo, J. M. et al. 2000. Long term dynamics of water and carbon in semi-arid ecosystems: an analysis in the Patagonian steppe. – Plant Ecol. 150: 133 – 143.

Peters, D. P. C. and Havstad, K. M. 2006. Nonlinear dynamics in arid and semiarid systems: interactions among drivers and processes across scales. – J. Arid Environ. 65: 196 – 206.

Reynolds, J. H. and Ford, E. D. 1999. Multi-criteria assessment of ecological process models. – Ecology 80: 538 – 553.

Reynolds, J. F. and Staff ord Smith, D. M. 2002. Global desertifi ca-tion: do humans cause deserts? Dahlem Workshop Report 88. – Dahlem Univ. Press.

Reynolds, J. F. et al. 2007. Global desertifi cation: building a science for dryland development. – Science 316: 847 – 851.

Rotundo, J. L. and Aguiar, M. R. 2005. Litter eff ects on plant regeneration in arid lands: a complex balance between seed retention, seed longevity and soil-seed contact. – J. Ecol. 93: 829 – 838.

Sankaran, M. et al. 2004. Tree-grass coexistence in savannas revis-ited – insights from an examination of assumptions and mech-anisms invoked in existing models. – Ecol. Lett. 7: 480 – 490.

Schlesinger, W. H. et al. 1990. Biological feedbacks in global deser-tifi cation. – Science 247: 1043–1048.

Scholes, R. J. and Archer, S. R. 1997. Tree-grass interactions in Savannas. – Annu. Rev. Ecol. Syst. 28: 517 – 544.

Semmartin, M. et al. 2004. Litter quality and nutrient cycling aff ected by grazing-induced species replacements along a pre-cipitation gradient. – Oikos 107: 149 – 161.

Supplementary material (available online as Appendix O20317 at � www.oikosoffi ce.lu.se/appendix � ). Appendix A1 – A3.

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